A company claims that the average life of a battery is 60 months. On a highway,

Question

A company claims that the average life of a battery is 60 months. On a highway, a mechanic while replacing those batteries for a sample of 200 cars mother the average life is 1720 days with a standard deviation of 450 days based on a mechanics sampled information
A) construct a 90% confidence interval estimate for the average life time of a battery? interpret it does the true average life claimed by the company fall in it?
B). construct a 95% confidence interval estimate for the average life time of a battery? interpret it does the true average life claimed by the company fall in it
C). Which confidence interval would you prefer? Why?

Explanation / Answer

average life of a battery , =60

sample size, n = 200

sample average, x = 1720 days = 1720/30 months = 57.33 months

standard deviation , s = 450 days= 450/30 month = 15 months

standard error, e = s/n = 15/200 = 1.06

A) at 90% confidence for a two tail distribution, z = 1.65 (from z table)

90% confidence interval estimate for the average life time of a battery = x ± (z*e)

=57.33 ± (1.65*1.06)

=(55.581, 59.079)

the true average life claimed by the company does not fall within the confidence interval.

B)

at 95% confidence for a two tail distribution, z = 1.96 (from z table)

95% confidence interval estimate for the average life time of a battery = x ± (z*e)

=57.33 ± (1.96*1.06)

=(55.2524, 59.4076)

the true average life claimed by the company does not fall within the confidence interval.

C) 95% confidence interval would be preferred over 90% as the interval is greater in 95%

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